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Axiom ax-addcl 8793
Description: Closure law for addition of complex numbers. Axiom 4 of 22 for real and complex numbers, justified by theorem axaddcl 8769. Proofs should normally use addcl 8815 instead, which asserts the same thing but follows our naming conventions for closures. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.)
Assertion
Ref Expression
ax-addcl  |-  ( ( A  e.  CC  /\  B  e.  CC )  ->  ( A  +  B
)  e.  CC )

Detailed syntax breakdown of Axiom ax-addcl
StepHypRef Expression
1 cA . . . 4  class  A
2 cc 8731 . . . 4  class  CC
31, 2wcel 1685 . . 3  wff  A  e.  CC
4 cB . . . 4  class  B
54, 2wcel 1685 . . 3  wff  B  e.  CC
63, 5wa 360 . 2  wff  ( A  e.  CC  /\  B  e.  CC )
7 caddc 8736 . . . 4  class  +
81, 4, 7co 5820 . . 3  class  ( A  +  B )
98, 2wcel 1685 . 2  wff  ( A  +  B )  e.  CC
106, 9wi 6 1  wff  ( ( A  e.  CC  /\  B  e.  CC )  ->  ( A  +  B
)  e.  CC )
Colors of variables: wff set class
This axiom is referenced by:  addcl  8815
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